A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities

We propose the use of a highly-accurate three-dimensional (3D) fully automatic hp-adaptive finite element method (FEM) for the characterization of rectangular waveguide discontinuities. These discontinuities are either the unavoidable result of mechanical/electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems. The proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi-analytical methods. It supports anisotropic refinements on irregular meshes with hanging nodes, and isoparametric elements. It makes use of hexahedral elements compatible with high-order H(curl)H(curl) discretizations. The 3D hp-adaptive FEM is applied for the first time to solve a wide range of 3D waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed.

Letters to the editor [An implementation of the Boundary Element Method for zoned media with stress discontinuities, T.J. Rudolphi, 1983]

En esta carta al editor, el profesor D. Enrique Alarcón Álvarez comenta el artículo de Thomas J. Rudolphi "An implementation of the Boundary Element Method for zoned media with stress discontinuities" publicado en la revista "International Journal for Numerical Methods in Engineering" Vol. 19, Nº 1, pags. 1–15, enero 1983.

Micromechanical basis for shear strength of rock discontinuities

The theoretical basis for evaluating shear strength in rock joints is presented and used to derive an equation that governs the relationship between tangential and normal stress on the joint during situations of slippage between the joint faces. The dependent variables include geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness. The effect roughness is studied, and the aforementioned formula is used to analyse joints under different conditions. A mathematical expression is deduced that explains Barton's value for the joint roughness coefficient (JRC) according to the roughness geometry. In particular, when the Hoek and Brown failure criterion is used for a rock in the contact with the surface roughness plane, it is possible to determine the shear strength of the joint as a function of the relationship between the uniaxial compressive strength of the wall with the normal stress acting on the wall. Finally, theoretical results obtained for the geometry of a three-dimensional joint are compared with those of the Barton's formulation